Yf. Dong et Hc. Gea, A NON-HYPERSINGULAR BOUNDARY INTEGRAL FORMULATION FOR DISPLACEMENT GRADIENTS IN LINEAR ELASTICITY, Acta mechanica, 129(3-4), 1998, pp. 187-205
Based on boundary displacement and traction, a non-hypersingular bound
ary integral formulation is developed for the displacement gradient. A
t an arbitrary boundary point where the displacement field at least sa
tisfies a Holder condition (u(k) is an element of C-1,C-gamma with gam
ma > 0), the displacement gradient can be calculated by the Cauchy Pri
ncipal Value (CPV) integration. The hypersingularity involved in conve
ntional formulation is circumvented by applying rigid body translation
. The numerical implementation of the present formulation is illustrat
ed, and both direct and indirect approaches are discussed. For two-dim
ensional problems, the coefficients involved in the direct approach ar
e analytically derived. The stress formulation is also discussed. Fina
lly, numerical examples are presented to validate the present formulat
ion.